Search Results

You are looking at 1 - 10 of 38 items for :

  • "rotations" x
  • Mathematics and Statistics x
  • All content x
Clear All

: Affine Differentialgeometrie Lehebel, P., Affine rotation surfaces and hypersurfaces, in: Geometry and Topology of Submanifolds (F. Dillen et al., editors), VIII. Proceedings on

Restricted access

Abstract  

Suppose that f: ℝ → ℝ is a given measurable function, periodic by 1. For an α ∈ ℝ put M n α f(x) = 1/n+1 Σk=0 n f(x + ). Let Γf denote the set of those α’s in (0;1) for which M n α f(x) converges for almost every x ∈ ℝ. We call Γf the rotation set of f. We proved earlier that from |Γf| > 0 it follows that f is integrable on [0; 1], and hence, by Birkhoff’s Ergodic Theorem all α ∈ [0; 1] belongs to Γf. However, Γf\ℚ can be dense (even c-dense) for non-L 1 functions as well. In this paper we show that there are non-L 1 functions for which Γf is of Hausdorff dimension one.

Restricted access
Restricted access

On the lattice discrepancy of ellipsoids of rotation Uniform Dist. Th. 4 101 – 114 .

Restricted access

805 Blokh, A., Misiurewicz, M. and Simányi, N. , Rotation sets of billiards with one obstacle, Commun. Math. Phys. , 266 (2006), 239–265. MR 2007i :37077

Restricted access

In this paper, we introduce a new concept of q-bounded radius rotation and define the class R*m(q), m ≥ 2, q ∈ (0, 1). The class R*2(q) coincides with S*q which consists of q-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.

Restricted access

Abstract

For a Banach space B of functions which satisfies for some m>0

∗
a significant improvement for lower estimates of the moduli of smoothness ω r(f,t)B is achieved. As a result of these estimates, sharp Jackson inequalities which are superior to the classical Jackson type inequality are derived. Our investigation covers Banach spaces of functions on ℝd or for which translations are isometries or on S d−1 for which rotations are isometries. Results for C 0 semigroups of contractions are derived. As applications of the technique used in this paper, many new theorems are deduced. An L p space with 1<p<∞ satisfies () where s=max  (p,2), and many Orlicz spaces are shown to satisfy () with appropriate s.

Restricted access

-007-7129-8 . [21] Nowak , W. G. 2009 On the lattice discrepancy of ellipsoids of rotation Unif. Distrib. Theory 4 101 – 114

Restricted access